Prior devices for transporting disabled or sick persons were problematic in that persons who had to be transported lying down could not be adequately secured, as conventional belts extending transversely across the stretcher or litter could not be relied upon to prevent the subject from continuing to move in a forward direction in the event of an accident. Since subjects are as a rule transported with their heads in the direction of movement, efforts were made to solve this problem by means of a head cushion fixed to the head end of a stretcher and/or mattress provided thereupon, with the subject's head and shoulder area to rest against said cushion. However, this solution likewise fails to provide sufficient safety and can possibly lead to a compression of the subject's spinal column. Furthermore, when a pillow of this kind is used, the subject can be transported only in a supine position, not on his side, as is sometimes necessary. Efforts have also been made to solve the above problem by means of complex suspender belt systems. Here again, however, it is impossible to transport the subject safely on his side. Moreover, the belt system is difficult to arrange, gets tangled easily, and, when fastened, impedes the attending physician in his efforts to gain access to the thorax of the subject, thus preventing the subject from receiving optimal care and treatment.